robert bristow-johnson <rbj@audioimagination.com> writes:

> On 1/11/14 10:06 AM, Randy Yates wrote:
>>
>> Well then of course they will be different. If signal vectors x1 != x2,
>> would you expect fft(x1) = fft(x2)?!?
>>
>> It is the data vector you should window, not the input to the FFT. If
>>
>>    L = NFFT,
>>
>> then of course they're one and the same.
>
> sorry, Randy.  didn't see you nail this until after i responded.

No problem, Robert. Sometimes I still answer again even though I see a
perfectly good answer because it may help to see a slightly different
POV and/or different words.
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

On 1/11/14 10:06 AM, Randy Yates wrote:
>
> Well then of course they will be different. If signal vectors x1 != x2,
> would you expect fft(x1) = fft(x2)?!?
>
> It is the data vector you should window, not the input to the FFT. If
>
>    L = NFFT,
>
> then of course they're one and the same.

sorry, Randy.  didn't see you nail this until after i responded.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On 1/11/14 8:14 AM, Marc Jenkins wrote:
> On 2014-01-07 18:20:19 +0000, robert bristow-johnson said:
>
>> On 1/7/14 11:06 AM, Marc Jenkins wrote:
>>> On 2014-01-06 03:06:17 +0000, robert bristow-johnson said:
>>>
>>>> also, Marc, you can (and, in my opinion, should) think of this
>>>> windowing and zero-padding as one single operations.
>>>>
>>>> before the operation you have x[n] for -inf < n < +inf
>>>>
>>>> after the operation you have x[n] * w[n] for the same n.
>>>>
>>>> both the truncation of x[n] to a specific length and the zero padding
>>>> can be modeled as zeros in the same w[n].
>>>>
>>>> then it doesn't matter what the order is.
>>>
>>> But why is there a tremendous difference in the FFT-result when changing
>>> the order?
>>>
>>
>> make sure it's the same w[n].
>
> What do you mean with that?

only what i said.

> Consider following pseude-matlab code:
>
> % Signal is y
> L = length(y);
> window = hann(L);
> NFFT = 2^nextpow2(L);
> y = [y; zeros(NFFT-L, 1)];

here, you stretched out y and made it longer.

> S = fft(y .* window, NFFT);

but you didn't zero-pad window.

you have to do this

L = length(y);
window = hann(L);
NFFT = 2^nextpow2(L);
y = [y; zeros(NFFT-L, 1)];
window = [window; zeros(NFFT-L, 1)];
S = fft(y .* window, NFFT);

and compare to your second case:

>
> vs.
>
> % Signal is y
> L = length(y);
> window = hann(L);
> y = y .* window;
> NFFT = 2^nextpow2(L);
> y = [y; zeros(NFFT-L, 1)];
> S = fft(y, NFFT);
>

but if you compare to this:

L = length(y);
NFFT = 2^nextpow2(L);
window = hann(NFFT);
y = [y; zeros(NFFT-L, 1)];
S = fft(y .* window, NFFT);

it's not the same window.


> These two variants clearly yield different results.

how?  you cannot make this test yield different results because you 
cannot make the multiplication by the window of a different length work. 
  MATLAB should flag that as an error.


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

Marc Jenkins <marc.jenkins@noreply.com> writes:

> On 2014-01-11 14:54:24 +0000, Randy Yates said:
>
>> Marc Jenkins <marc.jenkins@noreply.com> writes:
>>> [...]
>>> % Signal is y
>>> L = length(y);
>>> window = hann(L);
>>> NFFT = 2^nextpow2(L);
>>> y = [y; zeros(NFFT-L, 1)];
>>> S = fft(y .* window, NFFT);
>>
>> Unless the length of y is already a power of two, this should not even
>> run. The line
>>
>>   S = fft(y .* window, NFFT);
>>
>> should bomb out since you can't take the element-by-element
>> multiplication (.*) of two vectors of different lengths.
>
>
> You're right. But consider this two examples with the following window
> for the first
> window = hann(NFFT). That was what I meant.

Well then of course they will be different. If signal vectors x1 != x2,
would you expect fft(x1) = fft(x2)?!? 

It is the data vector you should window, not the input to the FFT. If

  L = NFFT, 

then of course they're one and the same.
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

On 2014-01-11 14:54:24 +0000, Randy Yates said:

> Marc Jenkins <marc.jenkins@noreply.com> writes:
>> [...]
>> % Signal is y
>> L = length(y);
>> window = hann(L);
>> NFFT = 2^nextpow2(L);
>> y = [y; zeros(NFFT-L, 1)];
>> S = fft(y .* window, NFFT);
> 
> Unless the length of y is already a power of two, this should not even
> run. The line
> 
>   S = fft(y .* window, NFFT);
> 
> should bomb out since you can't take the element-by-element
> multiplication (.*) of two vectors of different lengths.


You're right. But consider this two examples with the following window 
for the first
window = hann(NFFT). That was what I meant.

Marc

Marc Jenkins <marc.jenkins@noreply.com> writes:
> [...]
> % Signal is y
> L = length(y);
> window = hann(L);
> NFFT = 2^nextpow2(L);
> y = [y; zeros(NFFT-L, 1)];
> S = fft(y .* window, NFFT);

Unless the length of y is already a power of two, this should not even
run. The line

  S = fft(y .* window, NFFT);

should bomb out since you can't take the element-by-element
multiplication (.*) of two vectors of different lengths.

> vs.
>
> % Signal is y
> L = length(y);
> window = hann(L);
> y = y .* window;
> NFFT = 2^nextpow2(L);
> y = [y; zeros(NFFT-L, 1)];
> S = fft(y, NFFT);
>
> These two variants clearly yield different results. 

If the length of y is already a power of two, NFFT = L and the results
should be identical.

This is assuming nextpow2(L) = ceil(log2(L)).
-- 
Randy Yates
Digital Signal Labs
http://www.digitalsignallabs.com

On 2014-01-07 18:20:19 +0000, robert bristow-johnson said:

> On 1/7/14 11:06 AM, Marc Jenkins wrote:
>> On 2014-01-06 03:06:17 +0000, robert bristow-johnson said:
>> 
>>> also, Marc, you can (and, in my opinion, should) think of this
>>> windowing and zero-padding as one single operations.
>>> 
>>> before the operation you have x[n] for -inf < n < +inf
>>> 
>>> after the operation you have x[n] * w[n] for the same n.
>>> 
>>> both the truncation of x[n] to a specific length and the zero padding
>>> can be modeled as zeros in the same w[n].
>>> 
>>> then it doesn't matter what the order is.
>> 
>> But why is there a tremendous difference in the FFT-result when changing
>> the order?
>> 
> 
> make sure it's the same w[n].

What do you mean with that. Consider following pseude-matlab code:
% Signal is y
L = length(y);
window = hann(L);
NFFT = 2^nextpow2(L);
y = [y; zeros(NFFT-L, 1)];
S = fft(y .* window, NFFT);

vs.

% Signal is y
L = length(y);
window = hann(L);
y = y .* window;
NFFT = 2^nextpow2(L);
y = [y; zeros(NFFT-L, 1)];
S = fft(y, NFFT);

These two variants clearly yield different results. With the first one 
I get see spectrum peaks which I do not see with the second version - I 
want to understand what happens here.

Marc

On 1/8/14 12:00 AM, radams2000@gmail.com wrote:
> Great, for some reason I was getting errors for several days in a row (thought I was banned due to lame humor).

nobuddy gets band here, Bob.  maybe humiliated but there is no mechanism 
for banning in unmoderated USENET.  *maybe* the NNTP servers have a way 
of filtering out bot or spam posts.  i don't see them very much of late, 
so i imagine the NNTP servers have figured something out.


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."